Artificial rinds include waxed and cloth-wrapped rinds.
A cheese that comes in a waxy casing is packaged that way to seal the cheesy goodness in while it waits to be claimed and enjoyed. A waxed rind will usually surround semi-firm cheeses, like Gouda. This rind helps maintain the moisture in the cheese, and keeps anything from getting in, or out. The wax is food safe, but probably not very fun to eat.
A cloth-wrapped rind allows the cheese to breathe as it ages. This rind contributes to the flakey texture of the cheese it's protecting. We'd say don't eat this rind, but you do you.